Funnel MPC resolves the issue of requiring suitable terminal conditions (costs and constraints) in
the OCP (cf. [1]} and the references therein) or a sufficiently long prediction
horizon (cf. [2]}) in order to achieve recursive feasibility. This is achieved by a “funnel-like” stage cost, which penalizes the tracking error and grows unbounded when it approaches the funnel boundary. However, in the
Funnel MPC scheme proposed in [3]} output constraints were
incorporated in the OCP. It was then shown in [4]} that for the case of relative degree
one systems these constraints are superfluous and the funnel-inspired stage costs automatically
ensure initial and recursive feasibility. A generalization of these results to systems with relative
degree two was outlined in [5]}, however requiring a sufficiently long prediction horizon. In the present paper we extend the results
from [4]} to systems with arbitrary relative degree by designing a suitable stage cost
function, which is inspired by a recent funnel control design from [7]}.
